1. Technical Field
The present invention relates to a sampling apparatus, a sampling method, and a recording medium storing thereon a program. In particular, the present invention relates to a sampling apparatus, a sampling method, and a recording medium storing thereon a program for sampling a signal under measurement.
2. Related Art
A conventional sampling method, known as 2nd order sampling, uses two sampling timings having identical sampling frequencies and different phases, as shown in, for example, Arthur Kohlenberg, “Exact Interpolation of Band-limited Functions,” Journal of Applied Physics, Vol. 24, No. 12, December 1953. Sampling at N target points in each sampling cycle is also proposed, as in, for example, Kuroda Tohru, Kida Takuro, “Relations between the possibility of restoration of bandpass-type band-limited waves by interpolation and arrangement of sampling points”, Denki Tsushin Gakkai Ronbunsho, Vol J67-A, pp. 717-724, 1984.
With these conventional methods, N non-uniform sampling timings are set to one cycle. The continuous time function of the signal under measurement is then obtained by performing a convolution operation between sample data obtained by repeatedly sampling the signal under measurement over a plurality of cycles and the sampling function derived from the phase of each sampling timing. The discrete-time waveform data is obtained by sequentially substituting the discrete-time having the target time intervals into the continuous time function.
Since conventional methods require derivation of the sampling function and sequential calculation of the values of the waveform data by substituting time into the sampling function, the signal processing becomes complicated.
An interleave method is known for acquiring a signal having a high band by alternately and uniformly deviating sampling timings of a plurality of AD converters. With this method, however, the data amount acquired per unit time increases relative to the number of AD converters, and therefore the circuit size of the memory circuit at the final stage must be increased.
Another method is known for acquiring a signal having a high band by obtaining a signal that is down-converted by a mixer. With this method, however, a circuit such as a local oscillator and a filter must be provided, thereby increasing the circuit size.
Undersampling is yet another method for acquiring a signal having a high band. Undersampling, however, imposes a limit on the acquirable band. For example, if there is one AD converter, the acquirable signal is limited to having a bandwidth less than fs/2 and cannot cross multiples of (fs/2), where fs is the sampling frequency. Even if two AD converters perform undersampling through interleaving, a signal crossing a multiple of (fs/2) cannot be acquired.